1 Solar Wind During the Maunder Minimum Leif Svalgaard Stanford University Predictive Science, San Diego, 4 Sept. 2012

2 Indicators of Solar Activity Sunspot Number (and Area, Magnetic Flux) Solar Radiation (TSI, UV, …, F10.7) Cosmic Ray Modulation Solar Wind Geomagnetic Variations Aurorae Ionospheric Parameters Climate? More… After Eddy, 1976 Longest direct observations Rudolf Wolf Solar Activity is Magnetic Activity

3 Unfortunately Two Data Series Hoyt & Schatten, GRL 21, 1994 Ken Schatten

4 How Well was the Maunder Minimum Observed? H&S Number of days per year with ‘observations’ It is not credible that for many years there were not a single day without observations

5 More Realistic Assessment H&S 5% of 365 is ~20 days Even after eliminating the spurious years with ‘no missing data’ there are enough left to establish that the Maunder Minimum had very few visible sunspots and was not due to general lack of observations 1700

66 The Ratio Group/Zurich SSN has Two Significant Discontinuities At ~1946 (after Max Waldmeier took over) and at ~1885

7 Effect of Weighting of Sunspots Unweighted count red SSN = 10*G+S In the 1940s the observers in Zürich [and Locarno] began to Weight spots. The net result is a ~20% inflation of the official Zürich SSN since ~1945 Locarno Locarno is today the reference station of the official SIDC SSN Sergio Cortesi

8 Compared with Sunspot Area (obs) Not linear relation, but a nice power law with slope Use relation for pre-1945 to compute Rz from Area, and note that the observed Rz after 1945 is too high [by 21%]

99 Removing the discontinuity in ~1946, by multiplying Rz before 1946 by 1.20, yields Leaving one significant discrepancy ~1885

10 Wolf-Wolfer Groups Wolfer Wolf 80mm 64X 37mm 20X

11 Making a Composite Matched on this cycle Compare with group count from RGO [dashed line] and note its drift

12 Extending the Composite Comparing observers back in time [that overlap first our composite and then each other] one can extend the composite successively back to Schwabe: There is now no systematic difference between the Zurich SSN and a Group SSN constructed by not involving RGO.

13 K-Factors No correlation Why are these so different? 2% diff.

14 Why the large difference between Wolf and Wolfer? Because Wolf either could not see groups of Zurich classes A and B [with his small telescope] or deliberately omitted them when using the standard 80mm telescope. The A and B groups make up almost half of all groups

15 Removing the discontinuity in ~1885 by multiplying Rg by 1.47, yields Only two adjustments remove most of the disagreement and the evidence for a recent grand maximum ( )

16 The Effect on the Sunspot Curve No long-term trend the last 300 years SIDC

17 Removing the discrepancy between the Group Number and the Wolf Number removes the ‘background’ rise in reconstructed TSI I expect a strong reaction against ‘fixing’ the GSN from people that ‘explain’ climate change as a secular rise of TSI and other related solar variables

18 Typical Reconstruction TSI ~ TSI 0 +a·GSN + b· 11yr Now

19 Some More TSI Reconstructions Crucial question: is there a slowly varying background? I think not. Kopp/LASP

20 The Auroral Record in Europe 55º 43º 51º 45º 55º 60º It is very difficult [impossible?] to calibrate accurately the auroral record because of the unknown ‘civilization’ correction. Effect of Changing Magnetic Latitude Hungary S. Sweden Denmark

Year ‘Gleissberg Cycle’ in Solar Activity Asymmetry? Zolotova et al., 2010 Is this a ‘regular’ cycle or just over-interpretation of noisy data [like Waldmeier’s]? ‘Prediction’ from this: South will lead in cycle 25 or 26 and beyond. We shall see… Extreme Asymmetry during the Maunder Minimum… There are various dynamo theoretical ‘explanations’ of N- S asymmetry. E.g. Pipin, I can’t judge these…

22 Asymmetric Solar Activity 18

23 Comparing Cycles 14 and 24

24 Polar Field Reversal SC24 WSO

25 How do we Know that the Poles Reversed Regularly before 1957? Svalgaard, 1977 Wilcox & Scherrer, 1972 The predominant polarity = polar field polarity (Rosenberg-Coleman effect) annually modulated by the B-angle. This effect combined with the Russell- McPherron effect [geomagnetic activity enhanced by the Southward Component of the HMF] predicts a 22-year cycle in geomagnetic activity synchronized with polar field reversals, as observed (now for 1840s-Present). “Thus, during last eight solar cycles magnetic field reversals have taken place each 11 year period”. S-M effect. Vokhmyanin & Ponyavin, 2012

26 Cosmic Ray Modulation Depends on the Sign of Solar Pole Polarity Miyahara, 2011 The shape of the modulation curve [alternating ‘peaks’ and ‘flat tops’] shows the polar field signs. North pole Ice cores contain a long record of 10Be atoms produced by cosmic rays. The record can be inverted to yield the cosmic ray intensity. The technique is not yet good enough to show peaks and flats, but might with time be refined to allow this. Svalgaard & Wilcox, 1976

27 The Cosmic Ray Record Steinhilber et al oz/year 17 pounds/yr

28 Cosmic Ray Proxy [Berggren et al.]

29 24-hour running means of the Horizontal Component of the low- & mid- latitude geomagnetic field remove most of local time effects and leaves a Global imprint of the Ring Current [Van Allen Belts]: A quantitative measure of the effect can be formed as a series of the unsigned differences between consecutive days: The InterDiurnal Variability, IDV-index

30 IDV is strongly correlated with HMF B, but is blind to solar wind speed V

31 Space Climate Since we can reconstruct B, V, and n for 11 solar cycles we can determine an ‘average’ profile of the solar wind through the solar cycle

32 Solar Activity Sunspot Number Ap Geomagnetic Index (mainly solar wind speed) Heliospheric Magnetic Field at Earth

33 Since we can also estimate solar wind speed from geomagnetic indices [Svalgaard & Cliver, JGR 2007] we can calculate the radial magnetic flux from the total B using the Parker Spiral formula: There seems to be both a Floor and a Ceiling and most importantly no long- term trend since the 1830s. Variation of ‘Open Flux’

34 Floor and Ceiling of Solar Wind Alfvénic Mach number Ceiling Floor Observations seem to suggest that the magnitude of the solar cycle variation is invariant, i.e. does not depend on the size of the cycle. In particular, that the value at solar minimum is the same, ~12.25, in every cycle.

35 OMNI Explanation of M A Consider first the multi-species nature of the solar wind plasma: protons, alphas, electrons. We use subscripts p, a and e for these. N is density, T temperature, V flow speed, m mass Let Na = f*Np Ne = Np + 2*Na = Np*(1+2f) Mass density = mp*Np + ma*Na + me*Ne = mp*Np + 4*mp*f*Np = mp*Np * (1+4f) Thermal pressure = k * (Np*Tp + Na*Ta + Ne*Te) = k * (Np*Tp + f*Np*Ta + (1+2f)*Np*Te) = k*Np*Tp * [1 + (f*Ta/Tp) + (1+2f)*Te/Tp] Flow pressure = Np*mp*Vp**2 + Na*ma*Va**2 + Ne*me*Ve**2 = Np*mp*Vp**2 + f*Np*4*mp*Va**2 = Np*mp*Vp**2 * [l + 4f*(Va/Vp)**2] Rewrite: Mass density = C*mp*Np Thermal pressure = D*Np*k*Tp Flow pressure = E*Np*mp*Vp**2 Where C = 1+ 4f D = 1 + (f*Ta/Tp) + (1+2f)*Te/Tp E = 1 + 4f*(Va/Vp)**2 Now, some issues. 1. f is typically in the range , although there are significant differences for different flow types. 2. Ta/Tp is typically in the range What about Te? Feldman et al, JGR, 80, 4181, 1975 says that Te is almost always in the range 1-2*10**5 deg K. Te rises and falls with Tp, but with a much smaller range of variability. Kawano et al (JGR, 105, 7583, 2000) cites Newbury et al (JGR, 103, 9553, 1998) recommending Te = 1.4E5 based on ISEE 3 data. So we'll use Te = 1.4E5 deg K for our analysis. 4. What about (Va/Vp)**2? We should probably let this be unity always. If we let f=0.05, Ta=4*Tp, Va=Vp, and Te=1.4*10**5, we'd have C = 1.2 D = E5/Tp E = 1.2 Characteristic speeds: Sound speed = Vs = (gamma * thermal pressure / mass density)**0.5 = gamma**0.5 * [D*Np*k*Tp /C*mp*Np]**0.5 = gamma**0.5 * (D/C)**0.5 *(k*Tp/mp)**0.5 With the above assumptions for f, Ta, Va, and Te, and with gamma = 5/3, we'd get Vs (km/s) = 0.12 * [Tp (deg K) *10**5]**0.5 Alfven speed = VA = B/(4pi*mass_density)**0.5 = B/(4pi*C*mp*Np)**0.5 With the above assumptions, we'd get VA (km/s) = 20 * B (nT)/Np**0.5 and MA = V/Va = (V * Np**0.5) / 20 * B

36 For M A = 7.5 at all Maxima Question: Where would the MHD calculations fall in this diagram?

37 For M A = at all Minima M A =(V N p 0.5 )/(20 B) The marks the B = 4 nT contour of the ‘Floor’ in HMF

38 ‘Burning Prairie’ => Magnetism Foukal & Eddy, Solar Phys. 2007, 245,

39 Growing Deficiency of Sunspots

40 Deficit of Small Spots Large Small Lefevre & Clette, SIDC

41 The Livingston & Penn Data From 2001 to 2012 Livingston and Penn have measured field strength and brightness at the darkest position in umbrae of 1843 spots using the Zeeman splitting of the Fe nm line. Most observations are made in the morning [7h MST] when seeing is best. Livingston measures the absolute [true] field strength averaged over his [small: 2.5″x2.5″] spectrograph aperture, and not the Line-of-Sight [LOS] field. Temp.

42 Umbral Intensity [Temperature] and Magnetic Field

43 Evolution of Distribution of Magnetic Field Strengths Sunspots form by assembly of smaller patches of magnetic flux. As more and more magnetic patches fall below 1500 G, fewer and fewer spots will form

44 We see fewer sunspots for given MPSI MWO Plage Strength Index Calibration Change ? Cycle variation and Trend

45 Working Hypothesis The Maunder Minimum was not a deficit of magnetic flux, but A lessening of the efficiency of the process that compacts magnetic fields into visible spots This may now be happening again If so, there is new solar physics to be learned